We consider the light-cone (LC) gauge and LC quantization of the dimensional reduction of super Yang Mills theory from four to two dimensions. After integrating out all unphysical degrees of freedom, then on-local LC Hamiltonian exhibits an explicit \( \mathcal{N} = \left( {2,2} \right) \) supersymmetry. A further SUSY-preserving compactification of LC-space on a torus of radius R, allows for a large-N numerical study where the smooth large-R limit of physical quantities can be checked. As a first step, we consider a simple, yet quite rich, “Coulomb approximation” that maintains an \( \mathcal{N} = \left( {1,1} \right) \) subgroup of the original supersymmetry and leads to a non-trivial generalization of ’t Hooft’s model with an arbitrary –but conserved– number of partons. We compute numerically the eigenvalues and eigenvectors both in momentum and in position space. Our results, so far limited to the sectors with 2, 3 and 4 partons, directly and quantitatively confirm a simple physical picture in terms of a string-like interaction with the expected tension among pairs of nearest-neighbours along the single-trace characterizing the large-N limit. Although broken by our approximation, traces of the full \( \mathcal{N} = \left( {2,2} \right) \) supersymmetry are still visible in the low-lying spectrum.